Question

One solution of 10x^2 + bx – 3 = 0 is - 4/5 Find b and the other solution.

What is the value of b in the equation?​

Answer 1

see explanation

Explanation:

Given that x = -
`(4)/(5)` is a solution of the equation

Then substitute this value into the equation and solve for b

10 ( -
`(4)/(5)` )² + b(-
`(4)/(5)` ) - 3 = 0

10 ×
`(16)/(25)` -
`(4)/(5)` b - 3 = 0

`(32)/(5)` -
`(4)/(5)` b - 3 = 0

Multiply through by 5

32 - 4b - 15 = 0

17 - 4b = 0 ( subtract 17 from both sides )

- 4b = - 17 ( divide both sides by - 4 )

b =
`(17)/(4)` ← value of b

Given α and β are the roots of a quadratic equation, then

α + β = -
`(b)/(a)`

let α = -
`(4)/(5)`, then with a = 10 and b = b

-
`(4)/(5)` + β = -
`((17)/(4) )/(10)` = -
`(17)/(40)`

β = -
`(17)/(40)` +
`(4)/(5)` =
`(3)/(8)`

Hence the other solution is x =
`(3)/(8)`